Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 24.1674291456 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.758422990\) \(a_{3}=+0.577350269\) \(a_{4}=+2.092051411\) \(a_{5}=-1.056020568\)
\(a_{6}=-1.015225986\) \(a_{7}=-1.507622230\) \(a_{8}=-1.920288307\) \(a_{9}=+0.333333333\) \(a_{10}=+1.856930845\)
\(a_{11}=+0.033949132\) \(a_{12}=+1.207846445\) \(a_{13}=-1.034271875\) \(a_{14}=+2.651037590\) \(a_{15}=-0.609693759\)
\(a_{16}=+1.284627694\) \(a_{17}=+0.526413786\) \(a_{18}=-0.586140997\) \(a_{19}=-1.581801263\) \(a_{20}=-2.209249320\)
\(a_{21}=-0.870426101\) \(a_{22}=-0.059696934\) \(a_{23}=-0.604417031\) \(a_{24}=-1.108678971\) \(a_{25}=+0.115179441\)
\(a_{26}=+1.818687442\) \(a_{27}=+0.192450090\) \(a_{28}=-3.154023214\) \(a_{29}=-0.258737950\) \(a_{30}=+1.072099523\)
\(a_{31}=-0.937480372\) \(a_{32}=-0.338630565\) \(a_{33}=+0.019600541\) \(a_{34}=-0.925658103\) \(a_{35}=+1.592080085\)
\(a_{36}=+0.697350470\) \(a_{37}=-1.383735452\) \(a_{38}=+2.781475706\) \(a_{39}=-0.597137145\) \(a_{40}=+2.027863949\)
\(a_{41}=-0.833164486\) \(a_{42}=+1.530577266\) \(a_{43}=+0.572092649\) \(a_{44}=+0.071023330\) \(a_{45}=-0.352006856\)
\(a_{46}=+1.062820803\) \(a_{47}=-0.102531171\) \(a_{48}=+0.741680145\) \(a_{49}=+1.272924790\) \(a_{50}=-0.202534176\)
\(a_{51}=+0.303925141\) \(a_{52}=-2.163749935\) \(a_{53}=+0.814424293\) \(a_{54}=-0.338408662\) \(a_{55}=-0.035850982\)
\(a_{56}=+2.895069340\) \(a_{57}=-0.913253385\) \(a_{58}=+0.454970759\) \(a_{59}=-0.546106889\) \(a_{60}=-1.275510689\)
\(a_{61}=-0.763429805\) \(a_{62}=+1.648487039\) \(a_{63}=-0.502540743\) \(a_{64}=-0.689171925\) \(a_{65}=+1.092212373\)
\(a_{66}=-0.034466041\) \(a_{67}=+0.783550204\) \(a_{68}=+1.101284703\) \(a_{69}=-0.348960336\) \(a_{70}=-2.799550222\)
\(a_{71}=-0.301723098\) \(a_{72}=-0.640096102\) \(a_{73}=+1.817250639\) \(a_{74}=+2.433192230\) \(a_{75}=+0.066498881\)
\(a_{76}=-3.309209564\) \(a_{77}=-0.051182466\) \(a_{78}=+1.050019684\) \(a_{79}=+0.843371709\) \(a_{80}=-1.356593268\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.465055586\) \(a_{83}=+1.378232749\) \(a_{84}=-1.820976152\) \(a_{85}=-0.555903785\)
\(a_{86}=-1.005980866\) \(a_{87}=-0.149382425\) \(a_{88}=-0.065192121\) \(a_{89}=+0.720877265\) \(a_{90}=+0.618976948\)
\(a_{91}=+1.559291271\) \(a_{92}=-1.264471503\) \(a_{93}=-0.541254545\) \(a_{94}=+0.180293168\) \(a_{95}=+1.670414669\)
\(a_{96}=-0.195508448\) \(a_{97}=-0.285385706\) \(a_{98}=-2.238340214\) \(a_{99}=+0.011316377\) \(a_{100}=+0.240961311\)

Showing 100 of 1228 available coefficients

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